Self-trapped electron states in nanotubes

We study numerically self-trapped (polaron) states of quasiparticles (electrons or holes) in a deformable nanotube formed by a hexagonal lattice, wrapped into a cylinder (carbon- and boron nitride-type nanotube structures). We present a Hamiltonian for such a system taking into account an electron–phonon interaction, and determine conditions under which the lowest energy states are polarons. We compute a large class of numerical solutions of this model for a wide range of the parameters. We show that at not-too-strong electron–phonon coupling, the system admits ring-like localized solutions wrapped around the nanotube (the charge carrier is localized along the nanotube axis and is uniformly distributed with respect to the azimuthal coordinate). At stronger coupling, solutions are localized on very few lattice sites in both directions of the nanotube. The transition from one type of solution to the other one depends on the diameter of the nanotube. We show that for the values of the carbon nanotube parameters, the polarons have a ring-like structure wrapped around the nanotube, with a profile resembling that of the nonlinear Schrödinger soliton.